Enjoying good food is also an important part of Japanese trip! Ramen is something you can not miss in Fukuoka. We went to Ichiran(一蘭) . It was quite an interesting experience; you have to buy the ticket from a vending machine, and order the flavor you like(available in Chinese!), then sit in a tiny cubicle (ensure you concentrate on eating ramen) to enjoy your ramen.
Of course, the BBQ is another you have to try. There is no other beef taste better than Japanese beef. Also, don't forget sweet desserts and strawberries.